Hypercubes circumscribed in hyperspheres: a constant growth ratio for volumes at large dimensions

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dc.creatorShabot-Marcos, N.
dc.creatorSandoval-Villalbazo, A.
dc.date2004-11-04
dc.date.accessioned2026-07-07T05:13:59Z
dc.date.available2026-07-07T05:13:59Z
dc.descriptionThis note shows that an interesting property arises when considering the relation between the hypersphere volumes at dimensions $n+1$ and $n$, if the hyperspheres circumscribe unitary hypercubes in $n+1$ and $n$ dimensions, respectively . In the limit of large $n$, the ratio $\frac{V_{n+1}}{V_{n}}$ is constant and equal to the irrational number $\sqrt{\frac{πe}{2}}$. Some consequences of this result are explored.
dc.description2 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0411106
dc.identifierhttp://arxiv.org/abs/math/0411106
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73114
dc.subjectMetric Geometry
dc.titleHypercubes circumscribed in hyperspheres: a constant growth ratio for volumes at large dimensions
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